Main Ring + Space charge effects WHAT and HOW … Alexander Molodozhentsev for AP_MR Group May 10,...
-
Upload
debra-gardner -
Category
Documents
-
view
212 -
download
0
Transcript of Main Ring + Space charge effects WHAT and HOW … Alexander Molodozhentsev for AP_MR Group May 10,...
Main Ring+ Space charge effects
WHAT and HOW …
Alexander Molodozhentsevfor AP_MR Group
May 10, 2005
MR Injection process
Basic MR-design:
Injection time (Wkin=3 GeV) to accumulate the required beam intensityfrom RCS is about 0.17sec (in the case when just 5% of the total RCSbeam intensity is injected into MR).
The revolution period at the injection energy for MR is 5.38e-6 sec.
Then the injection process for MR is about 31’500 turns.
Feb.15,2005
Space charge tracking
General recommendation for the space-charge simulations
1. Transverse space-charge nodes should be at least 10 (or more) per one betatron oscillation
MR…Qx,y ~ 22, CRING = 1567.5 m, then LTSC ~ 7.5 m (~200 per ring nodes)
Our choice: TSC after each element and after LDRIFT < 3 m (~900 nodes per MR)
2. Number of macro-particles should be at least 10 per one mesh-point
…for the transverse mesh 32x32 minimum required number of the macro particles should be 10’000.
Our choice: time optimization … Nmp 10000
Feb.15,2005
ORBIT-MPI (TEAPOT tracker)
Single Processor.... DELL Latitude D600: Intel Pentium Centrino, 1.4GHzLinux RedHat 9
MR, 3GeV
1turn
MacroParticles
1'000mp 5'000mp 10'000mp 20'000mp 50'000mp 10'000mp+ BeamPipe
Pair-wise 23' 592.66'
Brute-Force PIC
22.22' 32x32
25.15'
FFT-PIC 32x32 40x40 32x32 32x32
~ 7’ 12.3' 30.9' 15.8'
1000 turns
1.9 h 3.4 h 8.6 h 4.4 h
10'000 turns
~ 19 h ~ 34 h ~ 86 h ~ 44 h
Estimation of time for simulation
Feb.15,2005
Longitudinal Nbin = 32
Comparison…
ORBIT-MPI
(J.Holmes,ORNL)
1 turn ~ 7’ (CPU)
ACCSIM4 *
(F.Jones,TRIUMF)
1turn ~ 30’ (CPU)
UAL
(N.Malitsky,BNL)
1 turn ~ 22’ (CPU)
* Including ACCSIM post-processing
Desktop PC-LINUXSingle processor
Notebook – LINUXSingle processor
Notebook – LINUXSingle processor
Feb.15,2005
Conditions: wp2, SpCh – ON … Nppb = 3.3e14/8, RF - ON, CCSX - OFF
2nd order MAD8 matrix Drift-Kick-Drift-Kick scheme:Q_split = 2 (kicks=8)BM_split =1 (kicks=4)
2nd order MAD8 matrixTeapot tracker:QM: (kicks=2)BM: (kicks=2)
Transverse space charge
• Pair-wise sum calculates the Coulomb force on one particle by summing the force
over all other particles. This method requires ~(np)2 operations to calculate the kicks, where np is the number of macro-particles.
• Brute-force PIC a straight forward PIC implementation. The macro particles are binned on
a prescribed X-Y grid, the force at each grid point is calculated using the
binned particle distribution, the force on each particle is calculated by a bi- linear interpolation from the grid. The operation time is ~(nbin)4.
• FFT-PIC … FFT method is used to calculate the force on the grid using the binned
particle distribution. The computation time is ~2nbin(nbin)2.
Feb.15,2005
Longitudinal space charge
• General way:
- bins the longitudinal beam profile;
- calculates the longitudinal space charge force;
- applies a momentum kick, based on the space charge force to the macro particles.
… the longitudinal profile of the beam is used as a weighting factor for
the transverse space charge kicks.
Couping the longitudinal motion into the transverse one:
… the space charge force on a given macro-particles is scaled according to the longitudinal charge density at its position in the bunch.
ORBIT-MPI test tracking
Wkin = 3GeV, Npb = 3.3e14/8 (h1=9)
RF-ON
ChromCorrection SX - ON
H1=9, VRF1 = 280kVH2=18, VRF2 = 140kV
‘Bare’ wp: Qx = 22.333 / Qy = 20.77
Gaussian Transverse:100% = 54 mm.mradRMS ~ 6.7 mm.mrad
Uniform Longitudinal:(p/p)MAX = 0.004()MAX = 60 degree
NSYNCH ~ 400 turns
ORBIT-MPI: Gaussian T-distribution Uniform L-distribution
Gaussian Transverse:100% = 54 RMS ~ 6.7
Qx=22.333Qy=20.774
Uniform Longitudinal:(p/p)MAX = 0.004()MAX = 60 degree
After 200 turns
2Q x-2Q y
=3
4Qy=83
-Qx+2Qy
=19
4Qx=
89
3Qx=
67
Qx+2Q
y=64
Qx + Q
y =43
2Qx-Q
y=2
4
3Qy=62
2Qx +Q
y =65
Gaussian TransverseDistribution
Kicks number(QM&BM) = 2 (in code=2)
SpCh – ON
CCSX - ON
ORBIT-MPI (Teapot tracker) test tracking
100% = 54 RMS ~ 6.8
Qx=22.333Qy=20.774
UAL test tracking
CCSX - ON
SpCh - ON
Gaussian TDUniform LD
Qx=22.333Qy=20.774
Kicks numberQM = 8 (in code=2)BM = 4 (in code=1)
100% = 54 RMS ~ 6.8
Steps … INJECTION & Acceleration
• COD
RANDOM BM-error (BL)/(BL)0 and H/V shift of QM so that to get some realistic COD (xCOD, yCOD) < 0.7 mm (TDR) … observation NORMAL SEXTUPOLE resonances & NORMAL OCTUPOLE resonances
• Misalignment
TILT of Sextupole Magnets … observation SKEW SEXTUPOLE resonances
TILT of Quadrupole Magnets … observation LINEAR COUPLING (skew) resonance
• Correction of Resonances …